A path can be deformed slightly to be a generic path, that is \(B(\sigma )\)  is singular only for finitely many values of \(\sigma \) , [1]}.
We denote \(I =\lbrace  \sigma \in (-1,1) : B(\sigma ) \text{ is singular} \rbrace \) ,
where we assume that the end points \(B(- 1)\)  and \(B(+1)\)  are regular (\(w_\pm \)  are hyperbolic critical points).
Moreover, at any \(\sigma _0 \in I\)  the kernel of \(B(\sigma _0)\) 
is 1-dimensional,
and the single eigenvalue such that \(\lambda (\sigma _0)=0\) 
crosses zero transversally: \(\lambda ^{\prime }(\sigma _0)\ne 0\) .
One defines the spectral flow of a generic path as
\({\rm specflow}(B(\sigma )) \,\stackrel{\mbox{\tiny \textnormal {\raisebox {0ex}[0ex][0ex]{def}}}}{=}\,\sum _{\sigma _0 \in I} {\rm sign}(\lambda ^{\prime }(\sigma _0)).\) 
